One of Dr. Tanaka's most important contributions to gravitational physics is his systematic studies on gravity in the brane-worlds. In particular, a careful analysis of gravity on the Randall-Sundrum (RS) brane-world, done in collaboration with Dr. Jaume Garriga, attracted a lot of attention. In this work, they showed that the gravity in the RS-I model (in which there are two branes) is approximately a Brans-Dicke (scalar-tensor) theory, while that in the RS-II model (in which there is only one brane) approaches Einstein gravity in the large distances, and they showed that corrections to gravitational potential is O(1/r^3) and derived the correction term accurately for the first time.
About the RS-II model, it has been argued that this model manifests the AdS/CFT correspondence discussed in string theory, namely the RS-II brane-world is equivalent to `4-dimensional Einstein gravity with strongly coupled conformal field theories'. Dr. Tanaka proposed a conjecture that a static black hole does not exist on the brane. This conjecture is based on the observation that the quantum evaporation of a black hole on the brane would correspond to classical 5-dimensional dynamics of a bulk black hole intersecting the brane.
In addition to the above, there are many more achievements by Dr. Tanaka. To mention a few more, with Dr. Oriol Pujolas and Dr. Jaume Garriga, he did a pioneering calculation of the Casimir energy in the brane-world. With Dr. Antonino Flachi, he also clarified in detail the process of a mini black hole escaping from the brane for the first time.
Dr. Tanaka made many important contributions to theoretical studies of gravitational wave physics as well. With Dr. Yasushi Mino and Dr. Misao Sasaki, he derived the equation of motion of a particle on curved spacetime which includes the gravitational radiation reaction for the first time. This equation has become a basis for studies on gravitational radiation reaction. Recently, with Dr. Norichika Sago and some others, he has developed an efficient method to calculate the radiation reaction to the Carter constant. Dr. Tanaka also contributed to the gravitational wave data analysis. With Dr. Hideyuki Tagoshi he formulated a basis for hierarchical searches.