arXiv subjects

Mandar Patil

Publications and source records attributed to Mandar Patil.

At least 19 recordsLinked to original sources

arXiv2020

Extremal Kerr white holes as a source of ultra high energy particles

We consider a process where two identical massive particles fall inwards, starting from rest at infinity towards the extremal Kerr black hole, collide outside the event horizon in its vicinity and produce two massless particles. The center of mass energy of collision between the two particles diverges if one of the particle admits a specific critical value of the angular momentum and if the collision takes place at a location arbitrarily close to the event horizon. Assuming the isotropic emission of particles in the center of mass frame we show that one of the massless particles produced has divergent conserved energy comparable to the center of mass energy with probability slightly less than half. This particle enters the black hole event horizon which coincides with the Cauchy horizon, turns back, and emerges through the white hole event horizon into another asymptotic region in the maximal extension of Kerr spacetime. Since conserved energy is preserved in this process, it is perceived as a particle with divergent energy by the observer when it reaches infinity. Thus the extremal white hole appears to be a source of ultra high energy particles. Similar processes wherein collision takes place slightly inside the black hole event horizon or just outside or inside of white hole event horizon also produce high energy particles.

gr-qc↗

arXiv2019

Gravitational lensing signature of matter distribution around Schwarzschild black hole

In this work, we focus on the situation where a significant amount of matter could be located close to the event horizon of the central black hole and how it affects the gravitational lensing signal. We consider a simple toy model where the matter is concentrated in the rather small region between the inner photon sphere associated with the mass of central black hole and outer photon sphere associated with the total mass outside. If no photon sphere is present inside the matter distribution, then effective potential displays an interesting trend with maxima at inner and outer photon sphere, with a peak at inner photon sphere higher than that at outer photon sphere. In such a case we get three distinct set of infinitely many relativistic images and Einstein rings that occur due to the light rays that approach the black hole from a distant source and get reflected just outside the outer photon sphere, due to light rays that enter the outer photon sphere slightly above the outer peak and get reflected off the potential barrier inside the matter distribution and due to the light rays that get reflected just outside the inner photon sphere. This kind of pattern of images is quite unprecedented. We show that since relativistic images are highly demagnified, only three images are prominently visible from the point of observations in the presence of matter as opposed to only one prominent image in case of a single isolated black hole and also compute the time delay between them. This provides a smoking gun signature of the presence of matter lump around the black hole. We further argue that if the mass of the black hole inferred from the observation of the size of its shadow is less than the mass inferred from the motion of objects around it, it signals the presence of matter in the vicinity of the black hole.

gr-qc↗

arXiv2017

The First Detection of Gravitational Waves

This article deals with the first detection of gravitational waves by the advanced Laser Interferometer Gravitational Wave Observatory (LIGO) detectors on 14 September 2015, where the signal was generated by two stellar mass black holes with masses 36 $ M_{\odot}$ and 29 $ M_{\odot}$ that merged to form a 62 $ M_{\odot}$ black hole, releasing 3 $M_{\odot}$ energy in gravitational waves, almost 1.3 billion years ago. We begin by providing a brief overview of gravitational waves, their sources and the gravitational wave detectors. We then describe in detail the first detection of gravitational waves from a binary black hole merger. We then comment on the electromagnetic follow up of the detection event with various telescopes. Finally, we conclude with the discussion on the tests of gravity and fundamental physics with the first gravitational wave detection event.

gr-qc↗

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

Curious case of gravitational lensing by binary black holes: a tale of two photon spheres, new relativistic images and caustics

Binary black holes have been in limelight off late due to the detection of gravitational waves from coalescing compact binaries in the events GW150914 and GW151226. In this paper we study gravitational lensing by the binary black holes modeled as equal mass Majumdar-Papapetrou dihole metric and show that this system displays features that are quite unprecedented and absent in any other lensing configuration investigated so far. We restrict our attention to the light rays which move on the plane midway between the two identical black holes, which allows us to employ techniques developed for the equatorial lensing in spherically symmetric spacetimes. If distance between the two black holes is below a certain threshold value, the system admits two photon spheres. As in the case of single black hole, infinitely many relativistic images are formed due to the light rays which turn back from the region outside the outer (unstable) photon sphere, all of which lie beyond a critical angular radius with respect to the lens. However in the presence of the inner (stable) photon sphere, the effective potential now increases again and the light rays that enter the outer photon sphere can turn back, leading to the formation of a new set of infinitely many relativistic images, all of which lie below the critical radius from the lens mentioned above. As the distance between the two black hole increases, two photon spheres approach each other, merge and eventually disappear. In the absence of photon sphere, apart from the formation of a finite number of discrete relativistic images, the system remarkably admits a radial caustic, which has never been observed in the context of relativistic lensing before. Thus the system of binary black hole admits novel features both in the presence and absence of photon spheres. We discuss possible observational signatures and implications of binary black hole lensing.

gr-qc↗

arXiv2016

Infinite efficiency of collisional Penrose process: Can over-spinning Kerr geometry be the source of ultra-high-energy cosmic rays and neutrinos ?

The origin of the ultra-high-energy particles we receive on the Earth from the outer space such as EeV cosmic rays and PeV neutrinos remains an enigma. All mechanisms known to us currently make use of electromagnetic interaction to accelerate charged particles. In this paper we propose a mechanism exclusively based on gravity rather than electromagnetic interaction. We show that it is possible to generate ultra-high-energy particles starting from particles with moderate energies using the collisional Penrose process in an overspinning Kerr spacetime transcending the Kerr bound only by an infinitesimal amount, i.e., with the Kerr parameter $a=M(1+ε)$, where we take the limit $ε\rightarrow 0^+$. We consider two massive particles starting from rest at infinity that collide at $r=M$ with divergent center-of-mass energy and produce two massless particles. We show that massless particles produced in the collision can escape to infinity with the ultra-high energies exploiting the collisional Penrose process with the divergent efficiency $η\sim {1}/{\sqrtε} \rightarrow \infty$. Assuming the isotropic emission of massless particles in the center-of-mass frame of the colliding particles, we show that half of the particles created in the collisions escape to infinity with the divergent energies. To a distant observer, ultra-high-energy particles appear to originate from a bright spot which is at the angular location $ξ\sim {2M}/{r_{obs}}$ with respect to the singularity on the side which is rotating towards the observer. We show that the anisotropy in emission in the center-of-mass frame, which is dictated by the differential cross-section of underlying particle physics process, leaves a district signature on the spectrum of ultra-high-energy massless particles. Thus, it provides a unique probe into fundamental particle physics.

gr-qc↗

arXiv2015

Timescale for trans-Planckian collisions in Kerr spacetime

We make a critical comparison between ultra-high energy particle collisions around an extremal Kerr black hole and that around an over-spinning Kerr singularity, mainly focusing on the issue of the timescale of collisions. We show that the time required for two massive particles with the proton mass or two massless particles of GeV energies to collide around the Kerr black hole with Planck energy is several orders of magnitude longer than the age of the Universe for astro-physically relevant masses of black holes, whereas time required in the over-spinning case is of the order of ten million years which is much shorter than the age of the Universe. Thus from the point of view of observation of Planck scale collisions, the over-spinning Kerr geometry, subject to their occurrence, has distinct advantage over their black hole counterparts.

gr-qc↗

arXiv2014

How small can an over-spinning body be in general relativity?

The angular momentum of the Kerr singularity should not be larger than a threshold value so that it is enclosed by an event horizon: The Kerr singularity with the angular momentum exceeding the threshold value is naked. This fact suggests that if the cosmic censorship exists in our Universe, an over-spinning body without releasing its angular momentum cannot collapse to spacetime singularities. A simple kinematical estimate of two particles approaching each other supports this expectation and suggests the existence of a minimum size of an over-spinning body. But this does not imply that the geometry near the naked singularity cannot appear. By analyzing initial data, i.e., a snapshot of a spinning body, we see that an over-spinning body may produce a geometry close to the Kerr naked singularity around itself at least as a transient configuration.

gr-qc↗

arXiv2014

Destroying a near-extremal Kerr black hole with a charged particle: Can a test magnetic field serve as a cosmic censor?

We investigate effect of a test magnetic field on the process of destroying near-extremal Kerr black hole with a charged test particle. It has been shown that it would be possible to throw a charged test particle into the near extremal rotating black hole and make it go past the extremality i.e. turn Kerr black hole into the Kerr-Newmann naked singularity. Typically in an astrophysical scenario black holes are believed to be surrounded by a magnetic field. Magnetic field although small, affects motion of charged particles drastically due to the large Lorentz force, as the electromagnetic force is much stronger that the gravity. Thus a test magnetic field can affect the process of destroying black holes and restore the cosmic censorship in the astrophysical context. We show that a test magnetic field would act as a cosmic censor beyond a certain threshold value. We try to gauge the magnitude of the magnetic field by comparing its energy density with that of the change in the curvature induced by the test particle. We find that the magnetic field required in only as strong as or slightly stronger as compared to the value for which its effect of the background geometry is comparable to the tiny backreaction as that of the test particle. In such a case however one has to take take into account effect of the magnetic field on the background geometry, which is difficult to implement in the absence of any exact near-extremal rotating magnetized black hole solutions. We argue that magnetic field would still act as a cosmic censor.

gr-qc↗

arXiv2014

Particle acceleration by Majumdar-Papapetrou di-hole

We explore the multi-black hole spacetimes from the perspective of the ultra-high energy particle collisions. Such a discussion is limited to the spacetimes containing a single black hole so far. We deal with the Majumdar-Papapetrou solution representing a system consisting of two identical black holes in the equilibrium. In order to identify the conditions suitable for the process of high energy collisions, we consider particles confined to move on the equatorial plane towards the axis of symmetry with the zero angular momentum. We consider collision between the particles moving in opposite directions at the location midway between the black holes on the axis. We show that the center of mass energy of collision between the particles increases with the decrease in the separation between the black holes and shows divergence in the limit where the separation goes to zero. We estimate the size of the region close to the central point on the equatorial plane where it would be possible to have high energy collisions and show that this region has a reasonably large spatial extent. We further explore the process of high energy collisions with the general geodesics with arbitrary angular momentum on the equatorial plane away from the central point. Although in this paper we deal with theMajumdar-Papapetrou spacetime which serves as a toy example representing multiple black holes, we speculate on the possibility that the ultra-high energy collisions would also occur in the more general setting like colliding black holes, when distance between the black holes is extremely small, which can in principle be verified in the numerical relativity simulations.

gr-qc↗

arXiv2014

Time Delay between Relativistic Images as a probe of Cosmic Censorship

We study the time delay between successive relativistic images in gravitational lensing as a possible discriminator between various collapse end states and hence as a probe of cosmic censorship. Specifically we consider both black hole and naked singularity spacetimes admitting photon spheres where an infinite number of relativistic Einstein Rings can be formed at almost the same radius and naked singularity spacetimes without a photon sphere where multiple relativistic Einstein Rings can form almost up to the center of the lens. The metrics we have considered to sample these scenarios are the Schwarzschild black hole, Janis-Newman-Winicour (naked singularity with photon sphere), Joshi-Malafarina-Narayan, and Tolman-VI (naked singularities without photon sphere) which are a fair sample of the theoretical possibilities. We show that the differential time delay between the relativistic images for naked singularities without a photon sphere progressively decreases for the models we study as opposed to that for black holes and naked singularities with a photon sphere, where it is known to be roughly constant. This characteristic difference in the time delay between successive images for these two cases can be potentially exploited for a source with known intrinsic variability to discriminate between these scenarios even when the images are not spatially resolved.

gr-qc↗

arXiv2013

Finite escape fraction for ultrahigh energy collisions around Kerr naked singularity

We investigate here the issue of observability of high energy collisions around Kerr naked singu- larity and show that the results are in contrast with the Kerr black hole case. We had shown earlier that it would be possible to have ultrahigh energy collisions between the particles close to the loca- tion r = M around the Kerr naked singularity if the Kerr spin parameter transcends the unity by an infinitesimally small amount a $\rightarrow 1^+$. The collision is between initially ingoing particle that turns back as an outgoing particle due to angular momentum barrier, with another ingoing particle. We assume that two massless particles are produced in such a collision and their angular distribution is isotropic in the center of mass frame. We calculate the escape fraction for the massless particles to reach infinity. We show that escape fraction is finite and approximately equal to half for ultrahigh energy collisions. Therefore the particles produced in high energy collisions would escape to infinity providing signature of the nature of basic interactions at those energies. This result is in contract with the extremal Kerr black hole case where almost all particles produced in high energy collisions are absorbed by the black hole, thus rendering the collisions unobservable.

gr-qc↗

arXiv2013

Ultra-high energy collision with neither black hole nor naked singularity

We explore the collision between two concentric spherical thin shells. The inner shell is charged, whereas the outer one is either neutral or charged. In the situation we consider, the charge of the inner shell is larger than its gravitational mass, and the inside of it is empty and regular. Hence the domain just outside it is described by the overcharged Reissner-Nordstrom geometry whereas the inside of it is Minkowski. First, the inner shell starts to shrink form infinity with finite kinetic energy, and then the outer shell starts to shrink from infinity with vanishing kinetic energy. The inner shell bounces on the potential wall and collides with the ingoing outer shell. The energy of collision between these shells at "their center of mass frame" does not exceed the total energy of the system. By contrast, by virtue of the very large gamma factor of the relative velocity of the shells, the energy of collision between two of the constituent particles of these shells at their center of mass frame can be much larger than the Planck scale. This result suggests that the black hole or naked singularity is not necessary for ultra-high energy collision of particles.

gr-qc↗

arXiv2012

Acceleration of particles and shells by Reissner-Nordström naked singularities

We explore the Reissner-Nordström naked singularities with a charge $Q$ larger than its mass $M$ from the perspective of the particle acceleration. We first consider a collision between two test particles following the radial geodesics in the Reissner-Nordström naked singular geometry. An initially radially ingoing particle turns back due to the repulsive effect of gravity in the vicinity of naked singularity. Such a particle then collides with an another radially ingoing particle. We show that the center of mass energy of collision taking place at $r \approx M$ is unbound, in the limit where the charge transcends the mass by arbitrarily small amount $0<1-M/Q\ll1$.The acceleration process we described avoids fine tuning of the parameters of the particle geodesics for the unbound center of mass energy of collisions and the proper time required for the process is also finite. We show that the coordinate time required for the trans-Plankian collision to occur around one solar mass naked singularity is around million years while it is many orders of magnitude larger than Hubble time in the black hole case. We then study the collision of the neutral spherically symmetric shells made up of dust particles. In this case, it is possible to treat the situation by exactly taking into account the gravity due to the shells using Israel`s thin shell formalism, and thus this treatment allows us to go beyond the test particle approximation. The center of mass energy of collision of the shells is then calculated in a situation analogous to the test particle case and is shown to be bounded above. However, we find thatthe energy of a collision between two of constituent particles of the shells at the center of mass frame can exceed the Planck energy.

gr-qc↗

arXiv2012

Can strong gravitational lensing distinguish naked singularities from black holes?

In this paper we study gravitational lensing in the strong field limit from the perspective of cosmic censorship, to investigate whether or not naked singularities, if at all they exist in nature, can be distinguished from black holes. We study the gravitational lensing in the strong field regime in the JMN spacetime, a spherically symmetric geometry that contains a naked singularity and which matches smoothly with Schwarzschild metric beyond a finite radius. This metric is a toy model which was shown recently to be the end state of gravitational collapse. In the presence of the photon sphere gravitational lensing signature of this spacetime is identical to that of Schwarzschild black hole with infinitely many relativistic images and Einstein rings, all of them located beyond a certain critical angle from optic axis and the inner relativistic images all clumped together. However, in the absence of the photon sphere, which is the case for a wide range of parameter values in this spacetime, we show that we get finitely many relativistic images and Einstein rings spaced reasonably apart from one another, some of which can be formed inside the critical angle for the corresponding Schwarzschild black hole. This study suggests that the observation of relativistic images and rings might, in principle, allow us to unravel the existence of the naked singularity in the absence of the photon sphere. The results obtained here are in contrast with the earlier investigation on JNW naked singularities radial caustic was always present in the absence of photon sphere, while it is absent in JMN geometry. We also point out the practical difficulties that might be encountered in the observation of the relativistic images and suggest that new dedicated experiments and techniques must be developed in future for this purpose.

gr-qc↗

arXiv2012

Ultra-high energy particle collisions in a regular spacetime without blackholes or naked singularities

We investigate here the particle acceleration and collisions with extremely large center of mass energies in a perfectly regular spacetime containing neither singularity nor an event horizon. The ultra-high energy collisions of particles near the event horizon of extremal Kerr blackhole, and also in many other examples of extremal blackholes have been investigated and reported recently. We studied an analogous particle acceleration process in the Kerr and Reissner-Nordstrom spacetimes without horizon, containing naked singularities. Further to this, we show here that the particle acceleration and collision process is in fact independent of blackholes and naked singularities, and can happen in a fully regular spacetime containing neither of these. We derive the conditions on the general static spherically symmetric metric for such a phenomena to happen. We show that in order to have ultra-high energy collisions it is necessary for the norm of the timelike Killing vector to admit a maximum with a vanishingly small but a negative value. This is also a condition implying the presence of a surface with extremely large but nevertheless finite value of the redshift or blueshift. Conditions to have ultrahigh energy collisions and regular center imply the violation of strong energy condition near the center while the weak energy condition is respected in the region around the center. Thus the central region is surrounded by a dark energy fluid. Both the energy conditions are respected at the location where the high energy collisions take place. As a concrete example we then investigate the acceleration process in the spacetime geometry derived by Bardeen which is sourced by a non-liner self-gravitating magnetic monopole.

gr-qc↗

arXiv2012

Circular geodesics and accretion disks in Janis-Newman-Winicour and Gamma metric

We study here circular timelike geodesics in the Janis-Newman-Winicour and Gamma metric spacetimes which contain a strong curvature naked singularity and reduce to the Schwarzschild metric for a specific value of one of the parameters. We show that for both the metrics the range of allowed parameters can be divided into three regimes where structure of the circular geodesics is qualitatively different. It follows that the properties of the accretion disks around such naked singularities can be significantly different from those of disks around black holes. This adds to previous studies showing that if naked singularities exist in nature, their observational signature would be significantly different from that of the black hole.

gr-qc↗