The Horizon Energy of a Black Hole

We investigate the energy distribution of a black hole in various spacetimes as reckoned by a distant observer using the quasi-local energy approach. In each case the horizon mass of a black hole: neutral, charged or rotating, is found to be twice the irreducible mass observed at infinity. This is known as the Horizon Mass Theorem. As a consequence, the electrostatic energy and the rotational energy of a general black hole are all external quantities. Matter carrying charges and spins could only lie outside the horizon. This result could resolve several long-standing paradoxes related to known black hole properties; such as why entropy is proportional to area and not to volume, the information loss problem, the firewall problem, the internal structure and the thin shell model of a black hole.Comment: Contributed paper to the Fourteenth Marcel Grossmann Meeting on General Relativity, University of Rome "La Sapienza", Italy, 12 - 18 July 2015 (7 pages) arXiv admin note: text overlap with arXiv:1706.0176

Is There Unification in the 21st Century?

In the last 100 years, the most important equations in physics are Maxwell's equations for electrodynamics, Einstein's equation for gravity, Dirac's equation for the electron and Yang-Mills equation for elementary particles. Do these equations follow a common principle and come from a single theory? Despite intensive efforts to unify gravity and the particle interactions in the last 30 years, the goal is still to be achieved. Recent theories have not answered any question in physics. We examine the issues involved in this long quest to understand the ultimate nature of spacetime and matter.Comment: Lecture delievered in Conference in Honor of Murray Gell-Mann's 80th Birthday. February 24 - 26, 2010. Nanyang Executive Centre, Singapore. 10 page

Study of gossamer superconductivity and antiferromagnetism in the t-J-U model

The d-wave superconductivity (dSC) and antiferromagnetism are analytically studied in a renormalized mean field theory for a two dimensional t-J model plus an on-site repulsive Hubbard interaction $U$. The purpose of introducing the $U$ term is to partially impose the no double occupancy constraint by employing the Gutzwiller approximation. The phase diagrams as functions of doping $\delta$ and $U$ are studied. Using the standard value of $t/J=3.0$ and in the large $U$ limit, we show that the antiferromagnetic (AF) order emerges and coexists with the dSC in the underdoped region below the doping $\delta\sim0.1$. The dSC order parameter increases from zero as the doping increases and reaches a maximum near the optimal doping $\delta\sim0.15$. In the small $U$ limit, only the dSC order survives while the AF order disappears. As $U$ increased to a critical value, the AF order shows up and coexists with the dSC in the underdoped regime. At half filing, the system is in the dSC state for small $U$ and becomes an AF insulator for large $U$. Within the present mean field approach, We show that the ground state energy of the coexistent state is always lower than that of the pure dSC state.Comment: 7 pages, 8 figure