It is forbidden to study Torah on Tisha B’Ab. As the Shulhan Aruch cites, the verse in Tehillim speaks of the joy received from Torah learning – "Pikudeh Hashem Yesharim Mesameheh Leb" – and for this reason Torah study is prohibited on this day of mourning.
Some Halachic authorities suggested that the study of Sod (Kabbalah) should be allowed on Tisha B’Ab, based on the Gemara’s comment in Masechet Megila that one is permitted to study the esoteric areas of Torah only if "Libo Do’eg Alav" – one feels worry in his heart. Hacham Ovadia Yosef, however, flatly rejects this view, and maintains that the study of Sod also brings one joy and is therefore forbidden on Tisha B’Ab.
The Lebush (Rav Mordechai Yoffe, 1530-1612) documents the practice not to read Tehillim on Tisha B’Ab, and this custom is cited as Halacha by the Mishna Berura (Rav Yisrael Meir Kagan, 1839-1933). Hacham Ovadia adds that even if a person is unlearned and thus incapable of reading any other Torah text, he should not read Tehillim, and should instead find material in a language he understands that is appropriate for Tisha B’Ab. If one normally reads a daily section of Tehillim, the section for Tisha B’Ab should be read either the day before or the day after the fast.
It should go without saying that one must spend the day of Tisha B’Ab focused on the destruction of the Bet Ha’mikdash. And therefore one should certainly not read newspapers or periodicals, or listen to radio programs and the like, on the day of Tisha B’Ab. (It goes without saying that one should also avoid other forms of media, which are inappropriate even the rest of the year…) In general, one should refrain from activities that draw his attention away from the tragedy of the Hurban, as this must be the point of focus throughout the day of Tisha B’Ab.
Summary: It is forbidden to study Torah on Tisha B’Ab, including Kabbalah, and including reading Tehillim. One should spend the day focused on mourning the destruction of the Bet Ha’mikdash, and therefore one should refrain from reading newspapers or other material, listening to the radio, and so on.
