arXiv subjects

Parthapratim Pradhan

Publications and source records attributed to Parthapratim Pradhan.

At least 37 records · Page 2Linked to original sources

arXiv2018

Thermodynamic Properties of Kehagias-Sfetsos Black Hole \& KS/CFT Correspondence

We speculate on various thermodynamic features of the inner horizon~(${\mathcal H}^{-}$) and outer horizons~(${\mathcal H}^{+}$) of Kehagias-Sfetsos~(KS) black hole~(BH) in the background of Hořava Lifshitz gravity. We compute particularly the \emph{area product, area sum, area minus and area division} of the BH horizons. We find that they all are \emph{not} showing universal behavior whereas the product is a universal quantity~ [Pradhan P., \textit{Phys. Lett. B}, {\bf 747} (2015) {64}]. Based on these relations, we derive the area bound of all horizons. From the area bound we derive the entropy bound and irreducible mass bound for all the horizons~(${\mathcal H}^{\pm}$). We also observe that the \emph{First law} of BH thermodynamics and \emph {Smarr-Gibbs-Duhem } relations do not hold for this BH. The underlying reason behind this failure due to the scale invariance of the coupling constant. Moreover, we compute the \emph{Cosmic-Censorship-Inequality} for this BH which gives the lower bound for the total mass of the spacetime and it is supported by cosmic cencorship conjecture. Finally, we discuss the KS/CFT~(Conformal Field Theory) correspondence via a thermodynamic procedure.

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arXiv2018

$P-V$ Criticality of Conformal Gravity Holography in Four Dimensions

{We examine the critical behaviour i. e. $P-V$ criticality of conformal gravity~(CG) in an extended phase space in which the cosmological constant should be interpreted as a thermodynamic pressure and the corresponding conjugate quantity as a thermodynamic volume.} The main potential point of interest in CG is that there exists a {non-trivial} \emph{Rindler parameter ($a$)} in the {spacetime geometry. This geometric parameter has an important role to construct a model for gravity at large distances where the parameter "$a$" actually originates}. We also investigate the effect of the said parameter on the {black hole~(BH) \emph{thermodynamic} equation of state, critical constants, Reverse Isoperimetric Inequality,} {first law of thermodynamics, Hawking-Page phase transition and Gibbs free energy} for this BH. We speculate that due to the presence of the said parameter, there has been a deformation {in the shape} of {the} isotherms in the $P-V$ diagram in comparison with {the} charged-AdS~(anti de-Sitter) BH and {the} chargeless-AdS BH. Interestingly, we find {that} the \emph{critical ratio} for this BH is $ρ_{c} = \frac{P_{c} v_{c}}{T_{c}}= \frac{\sqrt{3}}{2}\left(3\sqrt{2}-2\sqrt{3}\right)$, which is greater than the charged AdS BH and Schwarzschild-AdS BH {i.e.} $ρ_{c}^{CG}:ρ_{c}^{Sch-AdS}:ρ_{c}^{RN-AdS} = 0.67:0.50:0.37$. The symbols are defined in the main work. Moreover, we observe that \emph{{the} critical ratio {has a constant value}} and {it is} independent of the {non-trivial} \emph{Rindler parameter ($a$)}. Finally, we derive {the} \emph{reduced equation of state} in terms of {the} \emph{reduced temperature}, {the} \emph{reduced volume} and {the} \emph{reduced pressure} respectively.

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arXiv2017

Circular Geodesics in Tidal Charged Black Hole

We study the existence and stability criteria for circular geodesics of spherically symmetric tidal charged black hole~(BH). We investigate in details the equatorial causal geodesics of the tidal charged BH in comparison with spherically symmetric Reissner-Nordström BH spacetime. We particularly focused on both the null circular geodesics and time-like circular geodesics. Using the effective potential diagram, we have compared the geodesic structure between two spacetimes. We have derived the ISCO~(innermost stable circular orbit), MBCO~(marginally bound circular orbit) and CPO~(circular photon orbit) for both the space-times. Moreover, we have derived the \emph{quasi-normal modes~(QNM) frequency} in the \emph{eikonal limit} for both the spacetimes via Lyapunov exponent. In the Appendix section, we have shown that a spherically symmetric tidal-charged BH can act as particle accelerators with ultra-high center-of-mass~(CM) energy in the limiting case of \emph{maximal BH tidal charge~($q$)} and it is possible when two neutral particles are colliding near the horizon.

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arXiv2017

CFT and Logarithmic Corrections to the Black Hole Entropy Product Formula

We examine the logarithmic corrections to the black hole (BH) entropy product formula of outer horizon and inner horizon by taking into account the \emph{effects of statistical quantum fluctuations around the thermal equilibrium} and \emph{via conformal field theory} (CFT). We argue that logarithmic corrections to the BH entropy product formula when calculated using CFT and taking into the effects of quantum fluctuations around the thermal equilibrium, the formula should \emph{not be universal} and it should also \emph{not be quantized}. These results have been explicitly checked by giving several examples.

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arXiv2017

Mass Independent Area (or Entropy) and Thermodynamic Volume Products in Conformal Gravity

In this work we investigate the thermodynamic properties of conformal gravity in four dimensions. We compute the \emph{area(or entropy) functional} relation for this black hole. We consider both de-Sitter (dS) and anti de-Sitter (AdS) cases. We derive the \emph{Cosmic-Censorship-Inequality} which is an important relation in general relativity that relates the total mass of a spacetime to the area of all the black hole horizons. Local thermodynamic stability is studied by computing the specific heat. The second order phase transition occurs at a certain condition. Various type of second order phase structure has been given for various values of $a$ and the cosmological constant $Λ$ in the Appendix. When $a=0$, one obtains the result of Schwarzschild-dS and Schwarzschild-AdS cases. In the limit $aM<<1$, one obtains the result of Grumiller space-time. Where $a$ is non-trivial Rindler parameter or Rindler acceleration and $M$ is the mass parameter. The \emph{thermodynamic volume functional} relation is derived in the \emph{extended phase space}, where the cosmological constant treated as a thermodynamic pressure and its conjugate variable as a thermodynamic volume. The \emph{mass-independent} area (or entropy) functional relation and thermodynamic volume functional relation that we have derived could turn out to be a \emph{universal} quantity.

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arXiv2017

Entropy Product Formula for Gravitational Instanton

We investigate the entropy product formula for various gravitational instantons. We speculate that due to the mass-independent features of the said instantons they are \emph{universal} as well as they are \emph{quantized}. For isolated Euclidean Schwarzschild black hole, these properties simply \emph{fail}.

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arXiv2017

Circular Orbits in the Taub-NUT and mass-less Taub-NUT Space-time

In this work we study the equatorial causal geodesics of the Taub-NUT (TN) space-time in comparison with \emph{mass-less} TN space-time. We emphasized both on the null circular geodesics and time-like circular geodesics. From the effective potential diagram of null and time-like geodesics, we differentiate the geodesics structure between TN spacetime and mass-less TN space-time. It has been shown that there is a key role of the NUT parameter to changes the shape of pattern of the potential well in the NUT spacetime in comparison with \emph{mass-less} NUT space-time. We compared the ISCO (innermost stable circular orbit), MBCO (marginally bound circular orbit) and CPO (circular photon orbit) of the said space-time with graphically in comparison with mass-less cases. Moreover, we compute the radius of ISCO, MBCO and CPO for \emph{extreme} TN black hole (BH). Interestingly, we show that these \emph{three radii} coincides with the Killing horizon i.e. the null geodesic generators of the horizon. Finally in Appendix-A, we compute the center-of-mass (CM) energy for TN BH and mass-less TN BH. We show that in both cases the CM energy is finite. For \emph{extreme} NUT BH, we have found that the diverging nature of CM energy. \emph{First}, we have observed that a non-asymptotic flat, spherically symmetric and stationary extreme BH is showing such feature.

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arXiv2017

Behavior of a test gyroscope moving towards a rotating traversable wormhole

The geodesic structure of the Teo wormhole is briefly discussed and some observables are derived that promise to be of use in detecting a rotating traversable wormhole indirectly, if it does exist. We also deduce the exact Lense-Thirring (LT) precession frequency of a test gyroscope moving toward a rotating traversable Teo wormhole. The precession frequency diverges on the ergoregion, a behavior intimately related to and governed by the geometry of the ergoregion, analogous to the situation in a Kerr spacetime. Interestingly, it turns out that here the LT precession is inversely proportional to the angular momentum ($a$) of the wormhole along the pole and around it in the strong gravity regime, a behavior contrasting with its direct variation with $a$ in the case of other compact objects. In fact, divergence of LT precession inside the ergoregion can also be avoided if the gyro moves with a non-zero angular velocity in a certain range. As a result, the spin precession frequency of the gyro can be made finite throughout its whole path, even very close to the throat, during its travel to the wormhole. Furthermore, it is evident from our formulation that this spin precession not only arises due to curvature or rotation of the spacetime but also due to the non-zero angular velocity of the spin when it does not move along a geodesic in the strong gravity regime. If in the future, interstellar travel indeed becomes possible through a wormhole or at least in its vicinity, our results would prove useful in determining the behavior of a test gyroscope which is known to serve as a fundamental navigation device.

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arXiv2017

Logarithmic Corrections to the Black Hole Entropy Product of ${\cal H}^{\pm}$ via Cardy Formula

We compute the logarithmic corrections to black hole (BH) entropy product of ${\cal H}^{\pm}$ \footnote{ ${\cal H}^{+}$ and ${\cal H}^{-}$ denote outer (event) horizon and inner (Cauchy) horizons} by using \emph{Cardy prescription}. We particularly apply this formula for \emph{BTZ BH}. We speculate that the logarithmic corrections to entropy product of ${\cal H}^{\pm}$ when computed \emph{via Cardy formula} the product should be neither \emph{mass-independent (universal)} nor be \emph{quantized}.

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arXiv2016

Enthalpy, Geometric Volume and Logarithmic correction to Entropy for Van-der-Waals Black Hole

If the negative cosmological constant is treated as a dynamical pressure and if the volume be its thermodynamically conjugate variable then the gravitational mass can be expressed as the total gravitational enthalpy rather than the energy. Under these circumstances, a new phenomena emerges in the context of extended phase space thermodynamics. We \emph{examine} here these features for recently discovered Van-der-Waal (VDW) black hole (BH) \cite{mann15} which is analogous to the VDW fluid. We show that the thermodynamic volume is \emph{greater} than the naive geometric volume. We also show that the \emph{Smarr-Gibbs-Duhem} relation is satisfied for this BH. Furthermore, by computing the thermal specific heat we find the local thermodynamic stability criterion for this BH. It has been observed that the BH does \emph{not} possess any kind of second order phase transition. This is an interesting feature of VDW BH by its own right. Moreover, we also derive \emph{Cosmic-Censorship-Inequality} for this class of BH. In addition finally, we compute the \emph{logarithmic correction} to the entropy of this BH due to the quantum fluctuations around the thermal equilibrium.

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arXiv2016

Area products for ${\cal H}^{\pm}$ in AdS space

We derive the thermodynamic products particularly area (or entropy) products of ${\cal H}^{\pm}$ for certain class of black holes in AdS space. We show by explicit and exact calculations that more complicated function of event horizon area and Cauchy horizon area is indeed mass-independent. This mass-independent quantities indicate that they \emph{could turn out to be an "universal" quantity} provided that they depends only on the quantized angular momentum, quantized charges, and cosmological constant respectively. Furthermore, these area (or entropy) product relations for several class of black holes in AdS space gives us strong indication to understanding the nature of non-extremal black hole entropy (both inner and outer) at the microscopic level. Moreover, we compute the Penrose's famous \emph{Cosmic Censorship Inequality} (which requires Cosmic-Censorship hypothesis) for these class of black holes in AdS space . Local thermodynamic stability has been discussed for these black holes and under certain condition certain black holes displayed second order phase transition.

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arXiv2016

Extremal limits and Bañados-Silk-West effect

A fascinating property of extremal Kerr black hole (BH) is that it could be act as a particle accelerator with infinite high center-of-mass (CM) energy \cite{bsw}. In this note, we would like to discuss about such fascinating result and to point out that this infinite energy at the event horizon comes solely due \emph{to the singular nature of the extremal limit}. We also show that a non-extremal Kerr BH can \emph{not} transform into extremal Kerr BH by the Bañados-Silk-West mechanism. Moreover, we discuss about three possible geometries (near extremal, purely extremal and near horizon of extremal Kerr) of this mechanism. We further prove that near extremal geometry and near horizon geometry, precisely extremal geometry of extremal Kerr BHs are qualitatively different. Near extremal geometry and near horizon geometry gives the CM energy is finite, whereas precisely extremal geometry gives the diverging energy. Thus, we can argue that extremal Kerr BH and non-extremal Kerr BH are quite distinct objects. Finally, we show that the CM energy of collisions of particles not only diverges at infinite red-shift surface ($r_{+}$) but it could also diverges at the ISCO ($r_{isco}$) or at the circular photon orbit ($r_{cpo}$) or at the marginally bound circular orbit ($r_{mbco}$) or at the Cauchy horizon i.e. at $r \equiv r_{isco}=r_{cpo}=r_{mbco}=r_{+}=r_{-}=M$.

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arXiv2016

Surface Area Products for Kerr-Taub-NUT Space-time

We examine properties of the inner and outer horizon thermodynamics of Taub-NUT (Newman-Unti-Tamburino) and Kerr-Taub-NUT (KTN) black hole (BH) in four dimensional \emph{Lorentzian geometry}. We compare and contrasted these properties with the properties of Reissner Nordstrøm (RN) BH and Kerr BH. We focus on "area product", "entropy product", "irreducible mass product" of the event horizon and Cauchy horizons. Due to mass-dependence, we speculate that these products have no beautiful quantization feature. Nor does it has any universal property. We further observe that the \emph{First law} of BH thermodynamics and \emph {Smarr-Gibbs-Duhem} relations do not hold for Taub-NUT (TN) and KTN BH in Lorentzian regime. The failure of these aforementioned features are due to presence of the non-trivial NUT charge which makes the space-time to be asymptotically non-flat, in contrast with RN BH and Kerr BH. The another reason of the failure is that Lorentzian TN and Lorentzian KTN geometry contains \emph{Dirac-Misner type singularity}, which is a manifestation of a non-trivial topological twist of the manifold. The black hole \emph{mass formula} and \emph{Christodoulou-Ruffini mass formula} for TN and KTN BHs are also computed. This thermodynamic product formulae gives us further understanding to the nature of BH entropy (inner and outer) at the microscopic level.

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arXiv2016

Area Functional Relation for 5D-Gauss-Bonnet-AdS Black Hole

We present \emph{area (or entropy) functional relation} for multi-horizons five dimensional (5D) Einstein-Maxwell-Gauss-Bonnet-AdS Black Hole. It has been observed by exact and explicit calculation that some complicated function of two or three horizons area is \emph{mass-independent} whereas the entropy product relation is \emph{not} mass-independent. We also study the local thermodynamic stability of this black hole. The phase transition occurs at certain condition. \emph{Smarr mass formula} and \emph{first law} of thermodynamics have been derived. This \emph{mass-independent} relation suggests they could turn out to be an \emph{universal} quantity and further helps us to understanding the nature of black hole entropy (both interior and exterior) at the microscopic level. In the \emph{Appendix}, we have derived the thermodynamic products for 5D Einstein-Maxwell-Gauss-Bonnet black hole with \emph{vanishing} cosmological constant.

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arXiv2016

Thermodynamic Product Relations for Generalized Regular Black Hole

We derive thermodynamic product relations for four-parametric regular black hole (BH) solutions of the Einstein equations coupled with a non-linear electrodynamics source. The four parameters can be described by the mass ($m$), charge ($q$), dipole moment ($α$) and quadrupole moment ($β$) respectively. We study its complete thermodynamics. We compute different thermodynamic products i.e. area product, BH temperature product, specific heat product and Komar energy product respectively. Furthermore, we show that some complicated function of horizon areas that is indeed \emph{mass-independent} and could turn out to be \emph{universal}.

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arXiv2016

Thermodynamic Products in Extended Phase Space

We have examined the thermodynamic properties for a variety of spherically symmetric charged-AdS black hole (BH) solutions, including the charged AdS BH surrounded by quintessence dark energy and charged AdS BH in $f(R)$ gravity in \emph{extended phase-space}. This framework involves treating the cosmological constant as thermodynamic variable (for example: thermodynamic pressure and thermodynamic volume). Then they should behave as an analog of Van der Waal (VdW) like systems. In the extended phase space we have calculated the \emph{entropy product} and \emph{thermodynamic volume product} of all horizons. The mass (or enthalpy) independent nature of the said product signals they are \emph{universal} quantities. %Various type of phase diagram of the specific heat has been drawn. The divergence of the specific heat indicates that the second order phase transition occurs under certain condition. In the appendix-A, we have studied the thermodynamic volume products for axisymmetric spacetime and it is shown to be \emph{not universal} in nature. Finally, in appendix-B, we have studied the $P-V$ criticality of Cauchy horizon for charged-AdS BH and found to be an universal relation of critical values between two horizons as $P_{c}^{-} = P_{c}^{+}$, $v_{c}^{-}=v_{c}^{+}$, $T_{c}^{-} = -T_{c}^{+}$, $ρ_{c}^{-} = -ρ_{c}^{+}$. The symbols are defined in the main work.

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arXiv2016

Stability analysis and quasinormal modes of Reissner Nordstrøm Space-time via Lyapunov exponent

We explicitly derive the proper time $(τ)$ principal Lyapunov exponent ($λ_{p}$) and coordinate time ($t$) principal Lyapunov exponent ($λ_{c}$) for Reissner Nordstrøm (RN) black hole (BH) . We also compute their ratio. For RN space-time, it is shown that the ratio is $\frac{λ_{p}}{λ_{c}}=\frac{r_{0}}{\sqrt{r_{0}^2-3Mr_{0}+2Q^2}}$ for time-like circular geodesics and for Schwarzschild BH it is $\frac{λ_{p}}{λ_{c}}=\frac{\sqrt{r_{0}}}{\sqrt{r_{0}-3M}}$. We further show that their ratio $\frac{λ_{p}}{λ_{c}}$ may vary from orbit to orbit. For instance, Schwarzschild BH at innermost stable circular orbit(ISCO), the ratio is $\frac{λ_{p}}{λ_{c}}\mid_{r_{ISCO}=6M}=\sqrt{2}$ and at marginally bound circular orbit (MBCO) the ratio is calculated to be $\frac{λ_{p}}{λ_{c}}\mid_{r_{mb}=4M}=2$. Similarly, for extremal RN BH the ratio at ISCO is $\frac{λ_{p}}{λ_{c}}\mid_{r_{ISCO}=4M}=\frac{2\sqrt{2}}{\sqrt{3}}$. We also further analyse the geodesic stability via this exponent. By evaluating the Lyapunov exponent, it is shown that in the eikonal limit , the real and imaginary parts of the quasi-normal modes of RN BH is given by the frequency and instability time scale of the unstable null circular geodesics.

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arXiv2016

Logarithmic Corrections in Black Hole Entropy Product Formula

It has been shown by explicit and exact calculation that whenever we have taken the \emph{effects of stable thermal fluctuations} the entropy product formula should \emph{not be mass-independent} nor \emph{does it quantized}. It has been examined by giving some specific examples for non-rotating and rotating black hole.

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