Generalized second law of thermodynamics for a phantom energy accreting BTZ black hole

In this paper, we have studied the accretion of phantom energy on a (2+1)-dimensional stationary Banados-Teitelboim-Zanelli (BTZ) black hole. It has already been shown by Babichev et al that for the accretion of phantom energy onto a Schwarzschild black hole, the mass of black hole would decrease and the rate of change of mass would be dependent on the mass of the black hole. However, in the case of (2+1)-dimensional BTZ black hole, the mass evolution due to phantom accretion is independent of the mass of the black hole and is dependent only on the pressure and density of the phantom energy. We also study the generalized second law of thermodynamics at the event horizon and construct a condition that puts an lower bound on the pressure of the phantom energy.Comment: 4 pages, accepted for publication in Gen. Relativ. Gra

Static Axisymmetric Einstein Equations in Vacuum: Symmetry, New Solutions and Ricci Solitons

An explicit one-parameter Lie point symmetry of the four-dimensional vacuum Einstein equations with two commuting hypersurface-orthogonal Killing vector fields is presented. The parameter takes values over all of the real line and the action of the group can be effected algebraically on any solution of the system. This enables one to construct particular one-parameter extended families of axisymmetric static solutions and cylindrical gravitational wave solutions from old ones, in a simpler way than most solution-generation techniques, including the prescription given by Ernst for this system. As examples, we obtain the families that generalize the Schwarzschild solution and the $C$-metric. These in effect superpose a Levi-Civita cylindrical solution on the seeds. Exploiting a correspondence between static solutions of Einstein's equations and Ricci solitons (self-similar solutions of the Ricci flow), this also enables us to construct new steady Ricci solitons

Charged Rotating BTZ Black Hole and Thermodynamic Behavior of Field Equations at its Horizon

In this paper, we study different cases of the charged rotating BTZ black hole with reference to their horizons. For the existence of these cases conditions on mass, charge and angular momentum of the black hole are obtained. It is also shown that the Einstein field equations for the charged rotating BTZ black hole at the horizon can be expressed as first law of thermodynamics, $dE=TdS+\Omega dJ+\Phi dq+P_{r}dA$.Comment: 12 pages, 3 figure

UJI TOKSISITAS BERBAGAI JENIS DAN KONSENTRASI DETERJEN TERHADAP TINGKAT KERUSAKAN INSANG DAN MORTALITAS IKAN MAS (Cyprinus carpio)

Toxicity is toxic relative character related with its potential to cause negative effect for living creature. Water pollution is the entrance of living creature, element, energy, and another component in water by human activity so that the water quality decreased into certain level which caused the water couldn’t function as the general function. The research purpose is to find out the influence of various kind and concentrate of detergent to gills corruptness and mortality of gold fish (Cyprinus carpio), to find out the detergent brand which has the highest level to gold fish gills corruptness and mortality, beside, the research aimed to find out the influence of combination of kind and concentrate of detergent to the corruption of fish gills and mortality of gold fish. The research was true experimental research. The experiment design used complete random design with 20 treatments, they were four kinds of detergents and each of detergent has 0.08 mg/L, 0.04 g/L, 0.07 g/L, 0.10 g/L, 0.13 g/L concentrates. While 4 detergents used were Attack, Rinso, Wings biru, dan Krim ekonomi. Sampling technique used to Simple Random Sampling. Research indicator was the level of fish gills corruption and mortality of gold fish.. Data analysis used two way ANAVA continued with Duncan’s Test 1%. According to two way ANAVA test, there showed that there is influence of detergent kind and concentrate to the level of gills corruptness and mortality of Gold fish (Cyprinus carpio). From the Duncan’s Test 1%, concentrate of Wings Biru brand 0.13 g/L had the highest influence to the level of gills corruptness and mortality of gold fish. Attack Detergent concentrate 0.008 had the smallest influence

Cardy-Verlinde formula for an axially symmetric dilaton-axion black hole

It is shown that the Bekenstein-Hawking entropy of an axially symmetric dilaton-axion black hole can be expressed as a Cardy-Verlinde formula. By utilizing the first order quantum correction in the Bekenstein-Hawking entropy we find the modified expressions for the Casimir energy and pure extensive energy. The first order correction to the Cardy-Verlinde formula in the context of axially symmetric dilaton-axion black hole are obtained with the use of modified Casimir and pure extensive energies.Comment: 9 pages, accepted for publication in IJT