Anisotropic Stars: Exact Solutions

We study the effects of anisotropic pressure on the properties of spherically symmetric, gravitationally bound objects. We consider the full general relativistic treatment of this problem and obtain exact solutions for various form of equations of state connecting the radial and tangential pressures. It is shown that pressure anisotropy can have significant effects on the structure and properties of stellar objects. In particular, the maximum value of 2M/R can approach unity (2M/R < 8/9 for isotropic objects) and the surface redshift can be arbitrarily large.