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Date : 07-11-2014  
  Black Hole Interior Mass Formula, Parthapratim Pradhan  
 Publishers Name : EPJC
Date : 06-05-2014  
We argue by explicit computations that, although the area product, horizon radii product, entropy product and \\emph {irreducible mass product} of the event horizon and Cauchy horizon are universal, the \\emph{surface gravity product}, \\emph{surface temperature product} and \\emph{Komar energy product} of the said horizons do not seem to be universal for Kerr-Newman (KN) black hole space-time. We show the black hole mass formula on the \\emph{Cauchy horizon} following the seminal work by Smarr\\cite{smarr} for the outer horizon. We also prescribed the \\emph{four} laws of black hole mechanics for the \\emph{inner horizon}. New definition of the extremal limit of a black hole is discussed.
  Lyapunov Exponent and Charged Myers Perry Spacetimes, Parthapratim Pradhan  
 Publishers Name : Eur. Phys. J. C (2013) 73:2477
Date : 10-06-2014  
We compute the proper time Lyapunov exponent for charged Myers Perry black hole spacetime and investigate the instability of the equatorial circular geodesics (both timelike and null) via this exponent. We also show that for more than four spacetime dimensions (N≥3), there are \\emph{no} Innermost Stable Circular Orbits (ISCOs) in charged Myers Perry black hole spacetime. We further show that among all possible circular orbits, timelike circular orbits have \\emph{longer} orbital periods than null circular orbits (photon spheres) as measured by asymptotic observers. Thus, timelike circular orbits provide the \\emph{slowest way} to orbit around the charged Myers Perry black hole.
  Lense-Thirring Precession in Plebański-Demiański spacetimes, Parthapratim Pradhan  
 Publishers Name : Eur. Phys. J. C (2013) 73:2536
Date : 28-04-2014  
An exact expression of Lense-Thirring precession rate is derived for non-extremal and extremal Pleba\\\'nski-Demia\\\'nski spacetimes. This formula is used to find the exact Lense-Thirring precession rate in various axisymmetric spacetimes, like: Kerr, Kerr-Newman, Kerr-de Sitter etc. We also show, if the Kerr parameter vanishes in Pleba\\\'nski-Demia\\\'nski(PD) spacetime, the Lense-Thirring precession does not vanish due to the existence of NUT charge. To derive the LT precession rate in extremal Pleba\\\'nski-Demia\\\'nski we first derive the general extremal condition for PD spacetimes. This general result could be applied to get the extremal limit in any stationary and axisymmetric spacetimes.
  Extremal Limits and Kerr Spacetime, Parthapratim Pradhan and Parthasarathi Majumdar  
 Publishers Name : Eur. Phys. J. C (2013) 73:2470
Date : 20-06-2013  
The fact that one must evaluate the near-extremal and near-horizon limits of Kerr space-time in a specific order, is shown to a lead to discontinuity in the extremal limit, such that this limiting space-time differs nontrivially from the precisely extremal space-time. This is established by first showing a discontinuity in the extremal limit of the maximal analytic extension of the Kerr geometry, given by Carter. Next, we examine the ISCO of the exactly extremal Kerr geometry and show that on the event horizon of the extremal Kerr black hole, it coincides with the principal null geodesic generator of the horizon, having vanishing energy and angular momentum. We find that there is no such ISCO in the near-extremal geometry, thus garnering additional support for our primary contention. We relate this disparity between the two geometries to the lack of a trapping horizon in the extremal situation.
  Circular Orbits in Extremal Reissner Nordstrom Spacetimes, Parthapratim Pradhan, Parthasarathi Majumdar  
 Publishers Name : Phys.Lett.A375:474-479,2011
Date : 01-04-2010  
Circular null geodesic orbits, in extremal Reissner-Nordstrom spacetimes, are examined with regard to their stability, and compared with similar orbits in the near-extremal situation. Extremization of the effective potential for null circular orbits shows the existence of a stable circular geodesic in the extremal spacetime, precisely {\it on} the event horizon, which coincides with its null geodesic generator. Such an orbit also emerges as a global minimum of the effective potential for circular {\it timelike} orbits. This type of geodesic is of course absent in the corresponding near-extremal space-time, as we show here, testifying to differences between the extremal limit of a generic RN space-time and the exactly extremal geometry.
  Thermodynamic Product Formula for Hořava Lifshitz Black Hole, Parthapratim Pradhan  
 Publishers Name : Physics Letters B
Date : 30-07-2015  
We examine the thermodynamic properties of inner and outer horizons in the background of Ho\\v{r}ava Lifshitz black hole. We compute the \\emph{horizon radii product, the surface area product, the entropy product, the surface temperature product, the Komar energy product and the specific heat product} for both the horizons of said black hole. We show that surface area product, entropy product and irreducible mass product are \\emph{universal} quantities, whereas the surface temperature product, Komar energy product and specific heat product are \\emph{not universal} quantities because they all are depends on mass parameter. We also observe that the \\emph{First law} of black hole thermodynamics and \\emph {Smarr-Gibbs-Duhem } relations do not hold for this black hole. The underlying reason behind this failure due to the scale invariance of the coupling constant. We further derive the \\emph{Smarr mass formula} and \\emph{Christodolou-Ruffini mass formula} for such black hole spacetime. Moreover we study the stability of such black hole by computing the specific heat for both the horizons. It has been observed that under certain condition the black hole possesses second order phase transition.
  String Black Holes as Particle Accelerators to Arbitrarily High Energy, Parthapratim Pradhan  
 Publishers Name : Astrophysics and Space science
Date : 11-03-2014  
We show that an extremal Gibbons-Maeda-Garfinkle-Horowitz-Strominger black hole may act as a particle accelerator with arbitrarily high energy when two uncharged particles falling freely from rest to infinity on the near horizon. We show that the center of mass energy of collision independent of the extreme fine tuning of the angular momentum of the colliding particles. We further show that the center of mass energy of collisions of particles at the ISCO (rISCO) or at the photon orbit (rph) or at the marginally bound circular orbit (rmb) i.e. at r≡rISCO=rph=rmb=2M could be arbitrarily large for the aforementioned spacetimes, which is different from Schwarzschild and Reissner-Nordstr{\\o}m spcetimes. For non-extremal GMGHS spacetimes the CM energy is finite and depends upon the asymptotic value of the dilation field (ϕ0).
  Charged Dilation Black Holes as Particle Accelerators, Parthapratim Pradhan  
 Publishers Name : Astroparticle Physics
Date :  
We examine the possibility of arbitrarily high energy in the Center-of-mass(CM) frame of colliding neutral particles in the vicinity of the horizon of a charged dilation black hole(BH). We show that it is possible to achieve the infinite energy in the background of the dilation black hole without fine-tuning of the angular momentum parameter. It is found that the CM energy (Ecm) of collisions of particles near the infinite red-shift surface of the extreme dilation BHs are arbitrarily large while the non-extreme charged dilation BHs have the finite energy. We have also compared the Ecm at the horizon with the ISCO(Innermost Stable Circular Orbit) and MBCO (Marginally Bound Circular Orbit) for extremal Reissner-Nordstr{\\o}m(RN) BH and Schwarzschild BH. We find that for extreme RN BH the inequality becomes Ecm∣r+>Ecm∣rmb>Ecm∣rISCO i.e. Ecm∣r+=M:Ecm∣rmb=(3+5√2)M:Ecm∣rISCO=4M=∞:3.23:2.6. While for Schwarzschild BH the ratio of CM energy is Ecm∣r+=2M:Ecm∣rmb=4M:Ecm∣rISCO=6M=5√:2√:13√3. Also for Gibbons-Maeda-Garfinkle-Horowitz-Strominger (GMGHS) BHs, the ratio is being Ecm∣r+=2M:Ecm∣rmb=2M:Ecm∣rISCO=2M=∞:∞:∞.
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