arXiv subjects

Prashant Kocherlakota

Publications and source records attributed to Prashant Kocherlakota.

25 records · Page 2Linked to original sources

arXiv2019

An Approach to Stability Analyses in General Relativity via Symplectic Geometry

We begin with a review of the statements of non-linear, linear and mode stability of autonomous dynamical systems in classical mechanics, using symplectic geometry. We then discuss what the phase space and the Hamiltonian of general relativity are, what constitutes a dynamical system, and subsequently draw a formal analogy between the notions of stability in these two theories. Our approach here is pedagogical and geometric, and considerably simplifies a formal understanding of the statements regarding the stability of stationary solutions of general relativity. In particular, the governing equations of motion of a Hamiltonian dynamical system are simply the flow equations of the associated symplectic Hamiltonian vector field, defined on phase space, and the non-linear stability analysis of its critical points have simply to do with the divergence of its flow there. Further, the linear stability of a critical point is related to the properties of the tangent flow of the Hamiltonian vector field. Further, we posit that a study of the genericity of a particular black hole or naked singularity spacetime forming as an endstate of gravitational collapse is equivalent to an inquiry of how sensitive the orbits of the symplectic Hamiltonian vector field of general relativity are to changes in initial data. We demonstrate this by conducting a restricted non-linear stability analysis of the formation of a Schwarzschild black hole, working in the usual initial value formulation of general relativity.

gr-qc↗

arXiv2019

Gravitomagnetism and Pulsar Beam Precession near a Kerr Black Hole

A rotating black hole causes the spin-axis of a nearby pulsar to precess due to geodetic and gravitomagnetic frame-dragging effects. The aim of our theoretical work here is to explore how this spin-precession can modify the rate at which pulses are received on earth. Towards this end, we obtain the complete evolution of the beam vectors of pulsars moving on equatorial circular orbits in the Kerr spacetime, relative to asymptotic fixed observers. We proceed to establish that such spin-precession effects can significantly modify observed pulse frequencies and, in specific, we find that the observed pulse frequency rises sharply as the orbit shrinks, potentially providing a new way to locate horizons of Kerr black holes, even if observed for a very short time period. We also discuss implications for detections of sub-millisecond pulsars, pulsar nulling, quasi-periodic oscillations, multiply-peaked pulsar Fourier profiles and how Kerr black holes can potentially be distinguished from naked singularities.

astro-ph.HE↗

arXiv2019

A General Relativistic Approach to Small-Scale Structure Formation

We treat here general relativistically the issue of galaxy formation, which is a major problem in cosmology. While the current models use a top-hat collapse model, coupled with Newtonian virialization technique to balance the gravitationally collapsing matter cloud into a galaxy, we present here a general relativistic toy model to achieve such a purpose. We consider a relativistic gravitational collapse that begins from physically reasonable and non-singular initial conditions and that tends to an equilibrium configuration in asymptotic time. The matching of different spacetime regions is explicitly demonstrated to establish the feasibility of the model. This helps us understand better how the formation of galaxy-like objects and dark matter halos are likely to develop as the universe evolves, using a general relativistic technique. While the toy model we present here uses a somewhat simplistic collapse framework, this, however, has the potential to develop into a more realistic scenario, as we have noted. As we point out, the attractive feature here is, we have explicitly demonstrated that equilibrium configurations can be formed, with suitable matchings made, which go some way to treat the problem of galaxy formation within a full general relativity framework.

gr-qc↗

arXiv2018

Shadows of spherically symmetric black holes and naked singularities

We compare shadows cast by Schwarzschild black holes with those produced by two classes of naked singularities that result from gravitational collapse of spherically symmetric matter. The latter models consist of an interior naked singularity spacetime restricted to radii $r\leq R_b$, matched to Schwarzschild spacetime outside the boundary radius $R_b$. While a black hole always has a photon sphere and always casts a shadow, we find that the naked singularity models have photon spheres only if a certain parameter $M_0$ that characterizes these models satisfies $M_0\geq 2/3$, or equivalently, if $R_b\leq 3M$, where $M$ is the total mass of the object. Such models do produce shadows. However, models with $M_0<2/3$ (or $R_b>3M$) have no photon sphere and do not produce a shadow. Instead, they produce an interesting `full-moon' image. These results imply that the presence of a shadow does not by itself prove that a compact object is necessarily a black hole. The object could be a naked singularity with $M_0\geq 2/3$, and we will need other observational clues to distinguish the two possibilities. On the other hand, the presence of a full-moon image would certainly rule out a black hole and might suggest a naked singularity with $M_0<2/3$. It would be worthwhile to generalize the present study, which is restricted to spherically symmetric models, to rotating black holes and naked singularities.

astro-ph.HE↗

arXiv2017

On the stability of a superspinar

The superspinar proposed by Gimon and Horava is a rapidly rotating compact entity whose exterior is described by the over-spinning Kerr geometry. The compact entity itself is expected to be governed by superstringy effects, and in astrophysical scenarios it can give rise to interesting observable phenomena. Earlier it was suggested that the superspinar may not be stable but we point out here that this does not necessarily follow from earlier studies. We show, by analytically treating the Teukolsky equations by Detwiler's method, that in fact there are infinitely many boundary conditions that make the superspinar stable, and that the modes will decay in time. It follows that we need to know more on the physical nature of the superspinar in order to decide on its stability in physical reality.

gr-qc↗

arXiv2017

Distinguishing Kerr naked singularities and black holes using the spin precession of a test gyro in strong gravitational fields

We study here the precession of the spin of a test gyroscope attached to a stationary observer in the Kerr spacetime, specifically, to distinguish naked singularity (NS) from black hole (BH). It was shown recently that for gyros attached to static observers, their precession frequency became arbitrarily large in the limit of approach to the ergosurface. For gyros attached to stationary observers that move with non-zero angular velocity $Ω$, this divergence at the ergosurface can be avoided. Specifically, for such gyros, the precession frequencies diverge on the event horizon of a BH, but are finite and regular for NS everywhere except at the singularity itself. Therefore a genuine detection of the event horizon becomes possible in this case. We also show that for a near-extremal NS ($1 1.089$ for a certain range of $r$. For $1<a_*<1.089$, a peak appears, but the LT frequency remains positive definite. There are important differences in accretion disk LT frequencies for BH and NS and since LT frequencies are intimately related to observed QPOs, these features might allow us to determine whether a given rotating compact astrophysical object is BH or NS.

gr-qc↗

arXiv2017

Spin precession in a black hole and naked singularity spacetimes

We propose here a specific criterion to address the existence or otherwise of Kerr naked singularities, in terms of the precession of the spin of a test gyroscope due to the frame dragging by the central spinning body. We show that there is indeed an important characteristic difference in the behavior of gyro spin precession frequency in the limit of approach to these compact objects, and this can be used, in principle, to differentiate the naked singularity from black hole. Specifically, if gyroscopes are fixed all along the polar axis upto the horizon of a Kerr black hole, the precession frequency becomes arbitrarily high, blowing up as the event horizon is approached. On the other hand, in the case of naked singularity, this frequency remains always finite and well-behaved. Interestingly, this behavior is intimately related to and is governed by the geometry of the ergoregion in each of these cases which we analyze here. One intriguing behavior that emerges is, in the Kerr naked singularity case, the Lense-Thirring precession frequency ($Ω_{\rm LT}$) of the gyroscope due to frame-dragging effect decreases as ($Ω_{\rm LT}\propto r$) after reaching a maximum, in the limit of $r= 0$, as opposed to $r^{-3}$ dependence in all other known astrophysical cases.

gr-qc↗