arXiv subjects

V. H. Satheeshkumar

Publications and source records attributed to V. H. Satheeshkumar.

At least 19 recordsLinked to original sources

arXiv2026

What does a regular star look like?

Recently, astronomers discovered unusual Einstein cross images of the galaxy HerS-3, which feature a bright central spot. Motivated by studies of images produced by regular stars, it has been proposed that optical appearances caused by compact stars acting as gravitational lenses may account for this central bright spot. We further suggest that images produced by regular stars exhibit additional characteristics distinct from those of ordinary black holes, such as the possible partial or complete absence of secondary images. These phenomena may serve as favorable observational criteria for identifying regular stars in future searches.

gr-qc↗

arXiv2025

Complete Classification of Analytical Models in Einstein-Aether Cosmology

We present all possible analytical solutions of the Friedmann-Lemaître-Robertson-Walker metric in Einstein-aether theory for all values of the cosmological constant and spatial curvature with many reasonable values of the equation-of-state parameter. We analyze the dynamics of each model analytically and also graphically by plotting the geometric radius, Hubble and deceleration parameters along with the effective energy conditions. All our results are compared with the corresponding models in General Relativity. The two key results are (i) the aether does not qualitatively change the dynamics of the cosmological models but merely scales the geometric radius, Hubble, and deceleration parameters, and (ii) we found eight models that are entirely void of any aether, meaning in such a universe aether does not play any role cosmologically, although it affects the solar system dynamics.

gr-qc↗

arXiv2024

Cylindrical Gravitational Waves in Einstein-Aether Theory

Along the lines of the Einstein-Rosen wave equation of General Relativity (GR), we derive a gravitational wave equation with cylindrical symmetry in the Einstein-aether (EA) theory. We show that the gravitational wave in the EA is periodic in time for both the metric functions $Ψ(r,t)$ and $H(r,t)$. However, in GR, $Ψ(r,t)$ is periodic in time, but $H(r,t)$ is semi-periodic in time, having a secular drifting in the wave frequency. The evolution of wave pulses of a given width is entirely different in both theories in the $H(r,t)$ metric function due to this frequency drifting. Another fundamental difference between the two theories is the gravitational wave velocity. While in GR, the waves propagate with the speed of light, in EA, there is no upper limit to the wave velocity, reaching infinity if $c_{13} \rightarrow 1$ and zero if $c_{13} \rightarrow -\infty$. We also show that energy-momentum pseudotensor and superpotential get contributions from aether in addition to the usual gravitational field part. All these characteristics are observational signatures that differentiate GR and EA.

gr-qc↗

arXiv2023

Is Birkhoff's Theorem Valid in Einstein-Aether Theory?

We attempt to answer whether Birkhoff's theorem (BT) is valid in the Einstein-Aether (EA) theory. The BT states that any spherically symmetric solution of the vacuum field equations must be static, unique, and asymptotically flat. For a general spherically symmetric metric with metric functions $A(r,t)$ \& $B(r,t)$, and aether components $a(r,t)$ \& $b(r,t)$, we prove the conditions for the staticity of spacetime using two different methods. We point out that BT is valid in EA theory only for special values of $c_1+c_3$, $c_1+c_4$, and $c_2$, where we can show that all these special cases are asymptotically flat. In particular, when the aether has only a temporal component, i.e., $b(r,t)=0$ and the $c_{14} \neq 0$ case gives us spherically symmetric static black holes without horizons; that is, they have naked singularities, at least for special values of $c_{14}$. Thus, the cosmic censorship conjecture is violated for the case BT holds. However, when we have an aether vector with temporal and radial components, we only prove that the staticity and the flatness at infinity hold for a special metric and particular combination of the aether parameters. For this case, there exist universal horizons instead of naked singularities.

gr-qc↗

arXiv2022

Thermodynamics of Einstein-Aether Black Holes

We analyze several spherically symmetric exterior vacuum solutions allowed by the Einstein-Aether (EA) theory with a non static aether and study the thermodynamics of their Killing and universal horizons. We show that there are five classes of solutions corresponding to different values of a combination of the free parameters, $c_{2}$, $c_{13}=c_1+c_3$ and $c_{14}=c_1+c_4$, which are: (A) $c_2 \ne 0$ and $c_{13} \ne 0$ and $c_{14}=0$, (B) $c_2 \ne 0$ and $c_{13} = 0$ and $c_{14} = 0$, (C) $c_2 = 0$ and $c_{13} \ne 0$ and $c_{14} = 0$, (D) $c_2 = 0$, $c_{13} = 0$ and $c_{14} \ne 0$, and (E) $c_2 = - c_{13} \ne 0$ and $c_{14} \ne 0$. We present explicit analytical solutions for these five cases. All these cases have singularities at $r=0$ and are asymptotically flat spacetimes and possess both Killing and universal horizons with the universal horizons always being inside the Killing horizons. Finally, we compute the surface gravity, the temperature, the entropy and the first law of thermodynamics for the universal horizons.

gr-qc↗

arXiv2021

Nature of Singularities in Vector-Tensor Theories of Gravity

The Vector-Tensor (VT) theories of gravity are a class of alternative theories to General Relativity (GR) that are characterized by the presence of a dynamical vector field besides the metric. They are studied in attempts to understand spontaneous Lorentz violation, to generate massive gravitons, and as models of dark matter and dark energy. In this article, I outline how the nature of singularities and horizons in VT theories differ greatly from GR even under the same ordinary conditions. This is illustrated with Einsteinaether theory where vacuum black hole solutions have naked singularities and vacuum cosmological solutions have new singularities that are otherwise absent in GR. It would be interesting to explore these deviations using gravitational waves

gr-qc↗

arXiv2021

Spherically Symmetric Analytic Solutions and Naked Singularities in Einstein-Aether Theory

In the present work we analyze all the possible spherically symmetric exterior vacuum solutions allowed by the Einstein-Aether theory with static aether. We show that there are four classes of solutions corresponding to different values of a combination of the free parameters, $c_{14}=c_1+c_4$, which are: $ 0 < c_{14}<2$, $c_{14} < 0$, $c_{14}=2$ and $c_{14}=0$. We present explicit analytical solutions for $c_{14}=3/2, 16/9, 48/25, -16, 2$ and $0$. The first case has some pathological behavior, while the rest have all singularities at $r=0$ and are asymptotically flat spacetimes. For the solutions $c_{14}=16/9, 48/25\, \mathrm{\, and \,}\, -16$ we show that there exist no horizons, neither Killing nor universal horizon, thus we have naked singularities. Finally, the solution for $c_{14}=2$ has a metric component as an arbitrary function of radial coordinate, when it is chosen to be the same as in the Schwarzschild case, we have a physical singularity at finite radius, besides the one at $r=0$. This characteristic is completely different from General Relativity.

gr-qc↗

arXiv2020

Existence of New Singularities in Einstein-Aether Theory

How do the global properties of a Lorentzian manifold change when endowed with a vector field? This interesting question is tackled in this paper within the framework of Einstein-Aether (EA) theory which has the most general diffeomorphism-invariant action involving a spacetime metric and a vector field. After classifying all the possible nine vacuum solutions with and without cosmological constant in Friedmann-Lema{\^ı}tre-Robertson-Walker (FLRW) cosmology, we show that there exist three singular solutions in the EA theory which are not singular in the General Relativity (GR), all of them for $k=-1$, and another singular solution for $k=1$ in EA theory which does not exist in GR. This result is cross-verified by showing the focusing of timelike geodesics using the Raychaudhuri equation. These new singular solutions show that GR and EA theories can be completely different, even for the FLRW solutions when we go beyond flat geometry ($k=0$). In fact, they have different global structures. In the case where $Λ=0$ ($k=\pm 1$) the vector field defining the preferred direction is the unique source of the curvature.

gr-qc↗

arXiv2019

Vacuum solutions in the Einstein-Aether Theory

The Einstein-Aether (EA) theory belongs to a class of modified gravity theories characterized by the introduction of a time-like unit vector field, called aether. In this scenario, a preferred frame arises as a natural consequence of a broken Lorentz invariance. In the present work we have obtained and analyzed some exact solutions allowed by this theory for two particular cases of perfect fluid, both with Friedmann-Lemaitre-Robertson-Walker (FLRW) symmetry: (i) a fluid with constant energy density ($p=-ρ_0$), and (ii) a fluid with zero energy density ($ρ_0=0$), corresponding to the vacuum solution with and without cosmological constant ($Λ$), respectively. Our solutions show that the EA and GR theories do not differentiate each other only by the coupling constants. This difference is clearly shown because of the existence of singularities that there are not in GR theory. This characteristic appears in the solutions with $p=-ρ_0$ as well as with $ρ_0=0$, where this last one depends only on the aether field. Besides, we consider the term of the EA theory in the Raychaudhuri equation and discuss the meaning of the strong energy condition in this scenario and found that this depends on aether field. The solutions admit an expanding or contracting system. A bounce, a singular, a constant and an accelerated expansion solutions were also obtained, exhibiting the richness of the EA theory from the dynamic point of view of a collapsing system or of a cosmological model. The analysis of energy conditions, considering an effective fluid shows that the term of the aether contributes significantly for the accelerated expansion of the system for the case in which the energy density is constant. On the other hand, for the vacuum case ($ρ_0=0$), the energy conditions are all satisfied for the aether fluid.

gr-qc↗

arXiv2017

A Dynamical Solution in Horava-Lifshitz Gravity in the IR limit

Non-stationary null dust in a spherically symmetric spacetime is studied in the context of a general-covariant Horava-Lifshitz theory. The non-minimal coupling to matter is considered in the infrared limit. The aim of this paper is to study whether the collapse of a null dust-like fluid can be a solution of Hořava-Lifshitz theory in the infrared limit. We have shown that the unique possible solution is static. This solution represents a Minkowski spacetime since the energy density is null.

gr-qc↗

arXiv2017

Hilbert repulsion in the Reissner-Nordström and Schwarzschild spacetimes

Studying particle motion in the gravitational field of a black hole from the perspective of different observers is important for separating the coordinate artifacts from the physical phenomena. In this paper, we show that a freely falling test particle exhibits gravitational repulsion by a black hole as seen by an asymptotic observer, whereas nothing of the kind happens as recorded by a freely falling observer or by an observer located at a finite distance from the event horizon. This analysis is carried out for a general Reissner-Nordström, an extremal Reissner-Nordström, and a Schwarzschild black hole. We are lead to conclude that the origin of these bizarre results lies in the fact that the quantities measured by the different observers are neither Lorentz scalars nor gauge invariant.

gr-qc↗

arXiv2017

Can gravity be repulsive?

General Relativity has had tremendous successes on both theoretical and experimental fronts for over a century by now. However, the theory contents are far from being exhausted. Only very recently, with gravitational wave detection from colliding black holes, have we started probing gravity behavior in the strongly non-linear regime. Even today, black hole studies keep revealing more and more paradoxes and bizarre results. In this paper, inspired by David Hilbert's startling observation, we show that, contrary to the conventional wisdom, a freely falling test particle feels gravitational repulsion by a black hole as seen by an asymptotic observer. We dig deeper into this relativistic gravity surprising behavior and offer some explanations.

physics.gen-ph↗

arXiv2016

Troubles with the radiation reaction in electrodynamics

The dynamics of a radiating charge is one of the oldest unsettled problems in classical physics. The standard Lorentz-Abraham-Dirac (LAD) equation of motion is known to suffer from several pathologies and ambiguities. This paper briefly reviews these issues, and reports on a new model that fixes these difficulties in a natural way. This model is based on a hypothesis that there is an infinitesimal time delay between action and reaction. This can be related to Feynman's regularization scheme, leading to a quasi-local QED with a natural UV cutoff, hence without the need for renormalization as the divergences are absent. Besides leading to a pathology-free equation of motion, the new model predicts a modification of the Larmor formula that is testable with current and near future ultra-intense lasers.

hep-th↗

arXiv2016

Static and rotating universal horizons and black holes in gravitational theories with broken Lorentz invariance

In this paper, we show the existence of static and rotating universal horizons and black holes in gravitational theories with the broken Lorentz invariance. We pay particular attention on the ultraviolet regime, and show that universal horizons and black holes exist not only in low energy scales but also in the UV scales. This is realized by presenting various static and stationary exact solutions of the full theory of the projectable Hořava gravity with an extra U(1) symmetry in (2+1)-dimensions, which, by construction, is power-counting renormalizable.

gr-qc↗

arXiv2016

Quantization of 2D Hořava gravity: non-projectable case

The quantization of two-dimensional Hořava theory of gravity without the projectability condition is considered. Our study of the Hamiltonian structure of the theory shows that there are two first-class and two second-class constraints. Then, following Dirac we quantize the theory by first requiring that the two second-class constraints be strongly equal to zero. This is carried out by replacing the Poisson bracket by the Dirac bracket. The two first-class constraints give rise to the Wheeler-DeWitt equations, which yield uniquely a plane-wave solution for the wavefunction. We also study the classical solutions of the theory and find that the characteristics of classical spacetimes are encoded solely in the phase of the plane-wave solution in terms of the extrinsic curvature of the foliations $t =$Constant, where $t$ denotes the globally-defined time of the theory.

gr-qc↗

arXiv2015

Aspects of Black Holes in Gravitational Theories with Broken Lorentz and Diffeomorphism Symmetries

Since Stephen Hawking discovered that black holes emit thermal radiation, black holes have become the theoretical laboratories for testing our ideas on quantum gravity. This dissertation is devoted to the study of singularities, the formation of black holes by gravitational collapse and the global structure of spacetime. All our investigations are in the context of a recently proposed approach to quantum gravity, which breaks Lorentz and diffeomorphism symmetries at very high energies.

gr-qc↗

arXiv2015

Gravitational collapse in Hořava-Lifshitz theory

We study gravitational collapse of a spherical fluid in nonrelativistic general covariant theory of the Hořava-Lifshitz gravity with the projectability condition and an arbitrary coupling constant $λ$, where $|λ- 1|$ characterizes the deviation of the theory from general relativity in the infrared limit. The junction conditions across the surface of a collapsing star are derived under the (minimal) assumption that the junctions be mathematically meaningful in terms of distribution theory. When the collapsing star is made of a homogeneous and isotropic perfect fluid, and the external region is described by a stationary spacetime, the problem reduces to the matching of six independent conditions. If the perfect fluid is pressureless (a dust fluid), it is found that the matching is also possible. In particular, in the case $λ= 1$, the external spacetime is described by the Schwarzschild (anti-) de Sitter solution written in Painlevé-Gullstrand coordinates. In the case $λ\not= 1$, the external spacetime is static but not asymptotically flat. Our treatment can be easily generalized to other versions of Hořava-Lifshitz gravity or, more generally, to any theory of higher-order derivative gravity.

hep-th↗

arXiv2014

Spectral dimension of bosonic string theory

Given that the scale of quantum gravity is not experimentally accessible, one naturally resorts to mathematical consistency as a measure for a good candidate theory to replace General Relativity at high energies. Reproducing the semi-classical results of black hole entropy has become a standard test for any prospective theory of quantum gravity. It is often argued that another such commonality, albeit less known, is the similar fractal behaviour. It is shown that many, if not all, approaches to quantum gravity predict a spectral dimension of 2 in ultraviolet regime. In this paper, by computing the heat kernel, we show that the spectral dimension of closed bosonic string theory is 26. We discuss the implications of this disparity.

hep-th↗