## Research Interests

Research overviewMy main fields of interest are field theory, general relativity (GR), and theoretical cosmology. My interdisciplinary research has centered on black-hole physics, modified gravity (MG) models, quantum gravity (QG) phenomenology, and semi-classical gravity. Expanding GR to strong gravity regimes is crucial to understanding the early universe and Black-holes.

The group has developed and tested extensions to GR and field theory over the past decade. For instance, the polarization of the gravitational waves in MG Primordial Magnetic Fields led to baryogenesis and resolved black-hole problems through quantum entanglement. The following mind map gives a general overview of the group's recent research projects.

## Black holes (Theoretical aspect)

No hair theorem in MG theories

General Relativity (GR) continues to be, even after one hundred years, our best theory to describe the theory of gravitation. GR has passed every experimental test; however, it can not explain some astrophysical and cosmological observations without introducing new concepts like dark matter and dark energy. Over time, various attempts to modify GR as motivation for different reasons, like the desire to quantize gravity to unify it with the other three elementary known forces. f(R) gravity theories are the simplest extensions to GR. However, they contain non-linear higher-order derivatives of the metric, and hence, obtaining non-trivial exact solutions in these models is challenging.

No-hair conjecture asserts that all black holes in General Relativity (GR) coupled to any matter must be Kerr-Newman type. But, it is still unclear whether the no-hair theorem is a feature of gravity or GR. In other words, do modified gravity theories support other rotating BH solutions besides Kerr? If yes, which class of modified gravity theories supports and how are they different from the Kerr solutions in GR? It has been shown that the Kerr metric is not a solution for some modified theories of gravity containing scalar fields, like Chern-Simons. However, whether Kerr is a unique solution for metric theories containing higher-derivatives is unclear.

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Semin Xavier's thesis attempts to answer these questions for a class of f(R) gravity model. In the first work, we showed that the 4-D vacuum spherically symmetric space-time corresponding to f(R) gravity contains infinitely degenerate solutions. We then obtained two exact black-hole solutions with the event-horizon simultaneously. Thus, we confirmed that Birkhoff’s theorem is violated for f(R) gravity theories.

In the second work, we explicitly constructed multiple slowly rotating black hole (SRBH) solutions in a vacuum for a class of f(R) models. Thus, we confirmed that, in f(R) gravity, the generalized Bianchi identity provides a non-trivial structure for the Ricci scalar , leading to an infinite set of static, slowly rotating black hole solutions.

Evaporation rate of Primordial BH (PBH)

Astronomical and cosmological observations suggest that the universe is dominated by cold, non-baryonic dark matter. PBHs in the mass-range 10^17-10^23 gm are considered as possible dark matter candidates. This mass range is obtained for isolated stationary BHs. If PBHs are indeed dark matter, it is imperative to have a model that describes their evolution in the cosmological background and is surrounded by mass distributions. Unfortunately, no exact time-dependent solution has been found.

Recently, we filled this void and obtained an exact time-dependent solution that models evaporating black holes with a matter content described by a two-fluid source. Thus, the solution considers all three aspects of PBHs — Hawking radiation, black hole surrounded by mass distribution, and cosmological background. Furthermore, our model predicts that the decay rate of the PBHs occurs faster for larger masses, opposite to the black holes in asymptotically flat space-times. The proposed model has important implications for PBH constraints.Top

It is known that the Hawking temperature is inversely proportional to the BH mass, and the Kretschmann scalar describing the strength of the curvature is inversely proportional to the fourth power of the BH mass near its event horizon. These suggest that the above quantities become large at the end stage of the PBH evaporation. Therefore, the evaporation process of PBH is a high-energy process. As a result, we would also expect high-energy corrections to the Hawking temperature at the end stage of the evaporation process of PBHs. Therefore, this requires a systematic inclusion of the terms in action describing the evaporation process.

As a first step, models that can replicate 4-dimensional black holes in the classical limit and a systematic approach to incorporating high-energy corrections are necessary. For the first time, we derived the Callan, Giddings, Harvey, and Strominger model in (1+1) dimensions from the 4-dimensional Horndeski action. This action represents the most comprehensive scalar-tensor theory that avoids Ostrogradsky ghosts. Next, we showed that the 4-D Horndeski action can incorporate higher-derivative terms that are important during the later stages of black hole evaporation.

Tools to distinguish GR and modified gravity

According to GR, three measurable quantities (mass, charge, and angular momentum) fully characterize the isolated black holes in equilibrium. In other words, any deformations of the black-hole horizon will finally result in a black-hole configuration with the above three quantities~. Therefore, any object's material properties are unmeasurable as it collapses into or gets absorbed by a black-hole.

When two Black holes (BHs) merge to form another BH, the remnant BH's event horizon is highly distorted. It radiates gravitational waves (GWs) until it settles down to an equilibrium configuration~\cite{Vishu}. GWs emitted, referred to as quasi-normal modes (QNMs), are a superposition of damped sinusoids and depend only on the parameters characterizing the BH, namely, its mass and spin (astrophysical black holes are not likely to be electrically charged). QNMs are the fingerprints of the final BH. The simplicity of the spectrum allows one to identify the Kerr solution.

The video below provides a simple understanding of what happens when two BHs coallasce and form a new larger BH. (Courtesy: Youtube)Top

As mentioned above, GR is a hugely successful description of gravitation. However, both theory and observations suggest that General Relativity might have significant classical and quantum corrections in the Strong Gravity regime. Testing the strong field limit of gravity is one of the main objectives of the future gravitational wave detectors. One way to detect strong gravity is through the polarization of gravitational waves. For quasi-normal modes of black-holes in General Relativity, the two polarisation states of gravitational waves have the same amplitude and frequency spectrum. Will this be valid for modified gravity theories, and how can we use this to distinguish GR and MG?

For spherically symmetric black-holes without charge, we showed that this equality is not maintained in f(R) and Chern-Simons theories and obtained a quantifying tool to distinguish the same. We also extended the analysis for charged spherically symmetric black-holes and found a way to distinguish between the GR and modified theories of gravity. Using the principle of energy conservation , we showed that the polarisations differ for modified gravity theories. We obtained a diagnostic parameter for polarization mismatch that provides a unique way to distinguish General Relativity and modified gravity theories in gravitational wave detectors.

Black hole entropy and quantum entanglement

For over a decade, the group has been working on identifying the relation between two quantum effects --- entanglement entropy and black-hole entropy. The review discusses the deep connection between the two.

We identified new symmetries that entanglement entropy satisfies , which the Hamiltonian does not satisfy. These new symmetries play crucial role in removing the divergence of entanglement entropy. We also showed that entropy divergence, which was previously considered to be a UV divergence, actually occurs due to the generation of zero-modes in the system.Top

For the first time in literature, we established a one-to-one correspondence between entanglement energy, entropy, and temperature (entanglement mechanics) and the Komar energy, Bekenstein-Hawking entropy, and Hawking temperature of the horizon (black-hole thermodynamics), respectively. While this correspondence does not imply equality of their respective counterparts, they satisfy a universal relation, E=2TS, in perfect analogy with black-hole thermodynamics. By further extracting the Smarr-formula structure of black-holes directly from entanglement mechanics, we confirm that black-hole thermodynamics is of quantum origin. You can listen to the talk at IUCAA, here.

## Black holes (Observational aspect)

Testing Equivalence principle in VLBI observations

Einstein's general theory of relativity stands as the prevailing explanation for gravity today, having undergone successful validation through numerous observations and experiments. However, until recently, this theory was not thoroughly tested in the strong field regime. A notable shift occurred with the detection of gravitational waves by the Ligo-Virgo-Kagra collaboration and the imaging of a black hole's shadow by the Event Horizon Telescope. These groundbreaking observations have ushered in a new era for testing general relativity in intense gravitational environments, particularly near black holes.

To assess the theory, one can explore potential deviations from its fundamental principles, such as Einstein's equivalence principle (EEP). EEP asserts that the outcome of any local non-gravitational experiment in a freely falling laboratory remains unaffected by its velocity and position in space-time. In general relativity, the gravitational interaction with matter is described through minimal coupling, where the matter fields contribute to the energy-momentum tensor, which affects the curvature of space-time. Non-minimal coupling introduces additional terms in the equations of motion, allowing for a more complex interaction between the matter fields and gravity. The presence of non-minimally coupled fields, however, would violate EEP. In this study, we scrutinized the impact of a non-minimally coupled electromagnetic field on the images of black holes captured by VLBI telescopes.

The intense gravitational field near a black hole profoundly distorts space-time, creating an unstable orbit for photons encircling the black hole—a phenomenon perceived as a photon ring by distant observers. Without non-minimal coupling, the dimensions and configuration of this photon ring are determined by the black hole's characteristics, including its mass and spin.

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However, our research demonstrates that non-minimal coupling induces substantial alterations to the photon orbit and, consequently, the appearance of the observed photon ring. We analyzed within the Schwarzschild space-time, which characterizes a spherically symmetric black hole, and the Kerr space-time, describing rotating black holes commonly found at the centers of galaxies such as Sagittarius A* and M87.

We demonstrated that the two polarization modes of photons exhibit disparate behavior owing to non-minimal coupling. We explicitly illustrated that the non-minimal coupling brings about two distinct modifications to the black hole image: In the linear order in the spin parameter, the horizon produces a shadow with a larger radius for one mode and a smaller radius for the other mode than the minimally coupled photon. Additionally, the lensing ring's brightness and position are altered due to the non-minimal coupling. It has been determined that forthcoming VLBI observations can limit the NMC constant.

Detecting solitary Stellar mass black holes in our galaxy

Maxwell’s electrodynamics and Einstein’s general relativity are dynamic theories and have been tested with high precision. Solutions to Maxwell’s and Einstein’s equations lead to a rich diversity of phenomena, including the fields around static configurations and the generation of electromagnetic (EM) and gravitational radiation in various physical situations. However, the strong gravity regime close to black holes remains relatively unexplored.

Although laser interferometers will exploit gravitational wave (GW) information, our understanding of the large-scale universe is largely based on EM observations. Hence, the behavior of EM fields in strong gravity environments has attracted considerable interest over the years. While most studies address passive gravitational effects on the Maxwell field, relatively few examine the dynamics due to the interaction of EM fields in strong gravity backgrounds.

Susmita Jana's thesis is focused on exploiting these dynamics and providing novel ways to detect new phenomena in both EM and GW spectrum. Recently, with collaborators from the University of KwaZulu-Natal, we used this feature and showed that such dynamics could provide a route to detect the isolated BHs in our galaxy.

The work uses a gravitational analog of the Gertsenshtein Ze’ldovich (GZ) effect—conversion of EM waves into GWs or vice-versa in the presence of very high magnetic field. Specifically, we show that if an EM wave passes near a spherically symmetric compact object (like BHs), the curvature of the space-time acts analogous to the magnetic field that enables the GZ effect. We refer to this novel phenomenon, ‘gravitational analog to GZ effect,’ as the curvature (or gravity) associated with space-time facilitates the conversion of EM waves into GWs.

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The source of these incoming EM waves is Pulsars. Pulsars are known to radiate low-frequency EM waves with little variation, as they can be modeled using magnetic dipole. We show that when a kilohertz(kHz) EM pulse from a pulsar is intervened by a spherically symmetric compact object between the pulsar and Earth, GWs are generated. The emitted GWs have the same frequency as the incoming frequency of the EM wave. To entrench this phenomenon and relate it to astrophysical observations, we consider EM wave energy emitted from a typical pulsar (situated from a distance of 1 kpc from the BH) as predicted by the pulsar dipole model as 10^{38} erg. If the model prediction is correct, then the GW detector located on the Earth around (kpc from the BH) must produce a strain of 10^(-23). This amplitude is well in line with the expected sensitivity of the Einstein Telescope and Cosmic Explorer in the frequency range of 3-6 kHz. Thus, this opens a completely new way of detecting isolated stellar mass BHs.

Quantum gravitational/Modified Gravity signatures in GW spectrum

General Relativity (GR) continues to be our best theory to describe gravitation. GR has passed every experimental test. However, GR cannot explain some important astrophysical and cosmological observations without introducing new concepts such as dark matter and dark energy. Over time, various attempts to modify GR originate from attempts to quantize gravity and unify it with the three other fundamental forces of nature. However, the precise leading-order quantum gravitational corrections to GR at the strong-gravity regime are still unclear.

One consequence of combining gravity and quantum mechanics (Heisenberg's uncertainty principle) is the existence of a minimum length scale. The Generalized Uncertainty Principle (GUP) incorporates this fundamental length scale by adding momentum-dependent terms to the right-hand side of the standard uncertainty principle. A vast body of literature has studied the consequences of GUP for matter fields. However, to our knowledge, this has not been done for gravitons or spin-2 particles.

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Recently, for the first time, using Gupta-Feynman's approach to gravitation, we obtained an effective theory of gravity modified by GUP. Furthermore, we explicitly showed that this theory corresponds to a class of the well-known quadratic gravity models. Quadratic gravity is the most general second-order gravity theory in 4-D, and this class of quadratic gravity theories also contains degenerately massive scalar and tensor modes. Recently, we explicitly showed that the massive tensor modes, which are otherwise absent in the popularly studied f(R) and Chern-Simons theories of gravity, give the dominant correction to the gravitational waves. Furthermore, we analyzed the effect of the massive tensor modes on the energy flux measured by the gravitational wave detectors and the back reaction on the background space-time due to the emission of the gravitational waves.

Chern Simons (CS) gravity is a parity-violating strong field modification to GR with motivations arising from Loop Quantum Gravity and String theory and has important implications in Cosmology. The detection of Gravitational Waves (GWs) has provided an avenue to test for such modifications to GR. But how can the current or future GW detections distinguish between a rotating black hole solution of the CS theory and a Kerr black hole, its GR counterpart? Extracting QNM frequencies from the ringdown signals is one answer.

Recently, using an analytical approach, we computed the QNM frequencies of a slowly rotating black hole solution in dCS gravity, explicitly highlighting deviations from the slow rotating Kerr black hole. Interestingly, we showed that if the final BH mass is around 15 times the mass of the Sun, the dCS gravity corrections to QNMs are significant.

Indirect detection of high-frequency GWs

It took a century to directly detect gravitational waves (GWs) in the audio frequency range. However, in 1974, Hulse and Taylor indirectly detected GWs using electromagnetic (EM) waves in the radio frequency through the binary pulsar PSR B1913+16. The indirect detection used the age-old principle of energy conservation. It was discovered that the trajectory of a pulsar around a neutron star gradually contracts with time. This decay in the orbital period matches the loss of energy and momentum in the gravitational radiation predicted by general relativity and the energy released in the form of GWs.

GWs can be generated in various frequency ranges. In general, the characteristic frequency of the GW from a compact object is inversely related to object radius and directly related to mass. This raises an interesting question: Can one indirectly detect these high-frequency GWs? We showed that Neutron stars and Magnetars can act as laboratories for converting high-frequency GWs (HFGWs) to radio waves.

In the last decade, telescope and detector technology advancement enabled us to detect various transit and high-energy events such as Fast Radio Bursts (FRBs). FRBs are energetic and coherent and have short-span bursts, which were discovered in 2007. There were no unique physical mechanisms that could justify these observations. Recently, we provided a novel mechanism to explain FRBs using HFGWs in MHz and GHz.

TopThe model uses the Gertsenshtein-Zel'dovich effect --- conversion of GWs to EM waves in the presence of a strong transverse magnetic field. The model primarily has three ingredients --- a compact object, a progenitor with effective magnetic field strength around 10^9 Gauss, and MHz -GHz frequency GWs from astrophysical mechanisms. The energy conversion from GWs to electromagnetic waves occur when GWs pass through the magnetosphere of a Neutron star with a period range of 1-10⁻³ seconds due to the Gertsenshtein-Zel'dovich effect. This conversion produces bursts of EM waves, explaining the origin of FRBs.

A short article on the idea received an honorable mention in 2023-Gravity research essay competition.

## Cosmology (Theoretical aspect)

Helical magnetic fields and Baryogenesis

The present universe is observed to contain only matter and no antimatter. This asymmetry between baryons and antibaryons, also known as Baryon Asymmetry of the Universe is characterized by the parameter \eta_B ~ 10^{-10}. We still do not have a complete understanding of what caused this? However, in a remarkable paper in 1967, Sakharov pointed out that in order to have observed baryon asymmetry following conditions must be satisfied by any theory: (1) baryon number violation (2) charge and charge parity violation and (3) departure from thermal equilibrium.

As show in the above figure, observations from Faraday rotation and synchrotron radiation show the presence of micro-Gauss strength magnetic fields in the galaxies and the clusters of galaxies. While the magnetic field measurements from Faraday rotation and synchrotron radiation provide upper bounds of the magnetic fields, the FERMI measurement of gamma-rays emitted by blazars provides a lower bound of the order of 10^{-15}~Gauss in intergalactic voids. The origin of the magnetic field in these regions is still an open problem in modern cosmology; there is no compelling theoretical model to explain the generation of these large-scale magnetic fields.

The origin of primordial magnetic fields and origin of baryon asymmetry of the universe are the unresolved issues in modern cosmology and particle physics models. Both require physics beyond the standard model and pose an exciting question--- are these processes cosmological or particle physics or both?

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It seems impossible to generate the observed amount of baryon asymmetry within the Standard Model of particle physics framework. Since both require physics beyond the standard model, there is a possibility that the same physics can solve both problems. Part of Ashu Kushwaha's thesis was focused on this aspect. In two papers, he showed that the mechanism that leads to the generation of primordial helical magnetic fields also leads to baryogenesis at the beginning of the radiation-dominated epoch.

The electromagnetic field has two transverse degrees of freedom, i.e., left and right circular polarization, which can be associated with the left and right-handed helicity modes. Furthermore, modes having the same evolution (or dispersion relation) lead to the non-helical electromagnetic field, whereas differently propagating modes with non-zero net helicity imbalance give helical magnetic field. In order to create this helicity imbalance we considered an inflationary model to generate helical magnetic field from Riemann coupling. We showed that non-minimal coupling to the Riemann tensor generates sufficient primordial helical magnetic fields at all observable scales, which is free from the back-reaction problem. To our knowledge, Riemann tensor coupling has not been discussed in the literature to generate helical fields.

Using the fact that helical modes are generated at all length scales, we showed that the generation of helical magnetic fields from the above model leads to baryogenesis, particularly the modes entering just after the end of inflation provides the observed amount of baryon asymmetry. Furthermore, we showed that the baryon asymmetry parameter is independent of inflation models and depends only on the energy scale at the exit of inflation and reheating temperature.

Effective field theory of magnetogenesis

The origin of microGauss strength magnetic fields in the galaxies and clusters of galaxies is one of the long-standing problems in astrophysics and cosmology. These fields could have arisen from the dynamo amplification of seed fields. However, the dynamo mechanism needs seed magnetic fields. The key question is whether these seed magnetic fields were generated in the early Universe. The origin and detection of the seed magnetic fields is a subject of intense study.

Cosmological inflation has successfully provided a causal mechanism for generating large scale density perturbations and temperature fluctuations in the Cosmic microwave background. However, inflation can not provide the necessary amplitude for the seed magnetic field.Top

One reason is that the 4-dimensional electromagnetic action is conformally invariant. Several mechanisms have been proposed in the literature to break the conformal invariance of the electromagnetic action. All these mechanisms either require coupling of 4-vector potential to scalar field or breaking of gauge invariance, or introducing ghosts.

The group has been working on different proposals to generate primordial magnetic field during inflation, recombination and superinflation.

Recently, we proposed an Effective Field Theory (EFT) approach to unify these different approaches in the literature. We showed that the generation of primordial magnetic fields requires two conditions: conformal invariance breaking and causal propagation.

Tools to distinguish standard cosmology and modified gravity

Our current understanding of the cosmos is based on an enormous extrapolation of our limited knowledge of gravity since General Relativity has not been independently tested on galactic and cosmological scales. On the largest scales, the biggest surprise from observational cosmology has been that the current Universe is accelerating. The observations of Type Ia supernovae suggests that the current Universe is undergoing a phase of accelerated expansion which agrees with the observations of cosmic microwave background radiation.

Providing a fundamental understanding of the Universe's late-time accelerated expansion is one of the most challenging problems in cosmology. GR alone can not explain the late-time acceleration of the Universe with ordinary matter or radiation. The presence of an exotic matter source energy referred to as dark energy can explain the late-time accelerated expansion.

Joseph's thesis focus was to address obtain quantifying to tools to distinghuish GR and modified gravity in cosmological scales. For a general f(R) model, we considered a scenario where the accelerated expansion is due to modifications to gravity in the cosmological scales. Assuming that this is the same as the standard cosmology, we showed that the growth of structure formation would be different in these two cases.Top

To address the HO tension in cosmology, currently, we are looking at interacting dark energy (IDE) models, where dark matter (DM) and dark energy (DE) interact non-gravitationally. In the fluid picture, there is no restriction on the form of the interaction term. We addressed the important question: Can the field theory model provide correspondence to the fluid picture beyond the background expansion, i.e., at the level of cosmological perturbations?

## Cosmology (Observational aspect)

In Progress Top