arXiv:1006.3130v1 [gr-qc] 16 Jun 2010 ACCRETION OF HOLOGRAPHIC DARK ENERGY IN A GENERAL SPHERICALLY SYMMETRIC BLACK HOLE Ritabrata Biswas**, Nairwita Mazumder†, Subenoy Chakraborty* Department of Mathematics, Jadavpur University, Kolkata-32, India. [**biswas.ritabrata@gmail.com , †nairwita15@gmail.com,*schakraborty@math.jdvu.ac.in] Abstract The work deals with accretion of dark energy in the holographic dark en- ergy model for a general non-rotating static spherically symmetric black hole. The mass of the black hole increases or decreases depending on the nature of the holographic dark energy (quintessence or phantom) as well as on some integration parameters. Finally, generalized second law of thermodynamics has been examined on the event horizon. Key words: Black hole accretion, phantom energy, thermodynamics. 1 Introduction At present, it is strongly believed that our unverse is experiencing an accelerated expan- sion, starting at the cosmological red shift z ≃ 1. This accelerated expansion as predicted by recent cosmological observations obtained by SNeIa [1], WMAP [2], SDSS [3] and X-ray [4] is against the prediction from standard cosmology (based on Einstein’s general theory of relativity). To explain this unwanted observational fact within the framework of standard cosmology either one has to introduce non-baryonic matter (known as dark energy (DE)) having sufficient negative pressure so that strong energy condition (SEC ) (i.e., ρ +3p> 0) is violated in the framework of Einstein gravity or one has to use modi- fied gravity theory(such as f (r) gravity) where the extra terms in the modified Friedman equations are responsible for acceleration. In the framework of general relativity, the observational evidences demand that the matter in the universe is dominated by DE (about 74.5% of the energy content in ob- servable universe). Though cosmological constant is the simplest choice for DE candidate but it is not of much use due to fine-tuning problem[5]. The other candidates for dynam- ical DE are variable cosmological constant [6], canonical scalar field (quintessence) [7], a phantom field (negative K.E.)[8] or a unified model of quintessence and phantom field known as quintom [9] field. Recently, from an attempt to probe the nature of DE of the basis of some quantum gravitational principle is known as Holographic DE model(HDE) [10] Based on the holographic principle which states that the number of degrees of free- dom for a system within a finite region should be finite and is bounded roughly by the area of it boundary and from the effective quantum field theory, the holographic energy density is given by [11] ρD =3c 2 M 2 p L −2 . Where L is on IR cut-off in units of M 2 p = 1. Li [12, 13] shows that if we choose L as the radius of the future event horizon, then it is possible to have the correct equation of state and also the desired accelerating universe . Also in the above expression for ρD,c 1